You ask a bunch of questions there at the end. But I'm only going to address one and offer some unsolicited advice. 1) No, your conduct was not ethically justifiable. 2) Humans are fallible, particularly when we are young. You've learned from your mistake and done your best to make things right. It's time to move on from your demons.

@Ian, why not make that an answer?

Assuming the first article didn't actually claim the system was stable, there's no misconduct. Maybe slightly sharp practice in delaying the publication of the stability analysis that rendered the model irrelevant to physical reality. But in the end, the editor of the journal decided that a paper turning the handle on the model without a stability analysis was within scope; the referees decided that a paper turning the handle on the model without a stability analysis was of sufficient rigour; and the subsequent workers who used the results did so knowing the system hadn't been proved stable.

@DanielHatton Yes, neither the thesis nor the first article actually claimed the system was stable. I have edited the post to explicitly state that. I think your comment qualifies as an answer. At any rate, it reflects what I feel about the situation, so I am happy to see a confirmation of my perception.

"Is it ethically justifiable to conceal a critical conceptual flaw in a thesis if the flaw is the advisor's fault?" No, whose fault the flaw was has no bearing on your obligation not to knowingly disseminate flawed research. "Is it ethically justifiable to conceal a critical conceptual flaw in a thesis if doing so allows you to escape a country in a state of economic collapse and start an academic career in the West?" Perhaps. (In my opinion: yes, if the flawed research is not going to endanger anyone.) Are you sure you are asking the question that you actually want to ask?

I have a feeling you already knew the answer to this question, before you posted it.

Just chiming in here, I wouldn’t call it ethical but you can bet your ass I would have done the same under those circumstances. I generally don’t wanna compare bad things with worse things, but in this case: if this is your worst unethical behavior in life, I think you’re still ahead of most people.

Two more years for a mistake in a master's thesis? That sounds harsh, or at least different from the system I'm familiar with: where the master's is two years (nominally), but contains courses too, in addition to a (nominally) six-month(-ish) thesis. Even at worst, totally changing the subject of the thesis and redoing it from scratch would be six-month-ish setback.

Anyway, you mention there was an implicit assumption that the model was stable, and that it was popular and used for other purposes. So, how bad was it that it was unstable? From the way you put it, it doesn't seem it would have been totally unusable even with that issue, but I might be wrong? If it was popular and deemed usable, doing a master's research into it under the common assumptions seems normal. Not all master's theses can be groundbreaking, right?

Esp. if the system in your thesis was physically impossible anyway, some fault in it doesn't matter much. The thesis showed you were able to do the work on some subject, to the extent expected of a master's thesis. The fact that the work you did wasn't usable in practice or didn't include absolutely all viewpoints is irrelevant to that matter. On the other hand, if the instability wasn't well known, it might have been a useful thing to publish the finding that the system was/could be unstable, but of course refocusing the thesis on that would have also taken time, if even possible.

If you find yourself facing completely disproportionate consequences (lose the opportunity of a scientific career and a safer life abroad) for doing the right thing, then part of the fault lies with the system. This is why whistleblower protection is needed - we should encourage honesty and candour, not punish it. I know someone whose contract would not be renewed unless they produced some specific expected results. They would lose their visa and their whole family would be deported back to the country they had fled. The pressure to fabricate the expected results was immense.

@ilkkachu At that time and that university, the MS program was two years long. The research project had to be started at the very beginning of the two years and be based on a two-year research plan, which had to be signed by the student and the advisor at the very beginning. If I had elected to report the flaw, my research project would have been impossible to salvage. I would have had to sign an entirely new two-years research plan and spend two more years executing it. The university wouldn't have let me graduate within 6 or even 12 months of signing a research plan.

@Sandra, so, basically, everyone had to know from the beginning what the results would be two years later? Or at least that it was possible to get some results, that there wouldn't be any surprises in the meanwhile? Yeah, that doesn't sound exactly sane, IMO.

@Sandra I've been thinking about it, and no, my comment doesn't qualify as an answer: "there's no misconduct" does not imply "every decision that was made is ethically justifiable".

@ilkkachu Yes, at least according to the then-current regulations. The advisors were asked to come up with research projects whose outcomes and time frames were pretty predictable, because the main goal was training rather than groundbreaking discoveries. Also, it was allowed to modify the research plan during the project if intermediate results necessitated it. And it was also allowed to somewhat deviate from the signed plan if the deviation was not fundamental.

@ilkkachu I discovered a fatal conceptual flaw only 3 months before the thesis submission. The flaw invalidated all results I had obtained by then. Had I reported the flaw, I would have had no way of salvaging the project. I would have had to start an entirely new project and sign a plan for it, and no one would have let me complete it faster than 2 years from the date of signing. It was a very rigid system

@Sandra you need to clarify if an MS degree in Russia seen as undergraduate ? Here in EU an MS is seen as postgraduate, something taken after a BS, BEng, etc.

"Is this ethical?" questions in academia.SE are like "Is this a scam?" questions in money.SE. The answer is almost always the same, and it's not usually the answer the OP is hoping to hear.

@Trunk Yes, at that time MS students in Russia were seen as undegraduate students despite them having a BS degree.

@Trunk Almost everyone who got a BS went on to get an MS. A BS was seen as an incomplete qualification. I have edited the 1st sentence of my post to say that I graduated from a Russian university with an MS, i.e., graduation = MS